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Dynamical Analysis of a One- and Two-Scroll Chaotic System

Author

Listed:
  • Meng Liu

    (Jiaxing Nanyang Polytechnic Institute, Jiaxing 314003, China)

  • Zhaoyan Wu

    (School of Mathematics and Statistic, Jiangxi Normal University, Nanchang 330022, China
    Jiangxi Provincial Center of Applied Mathematics, Jiangxi Normal University, Nanchang 330022, China)

  • Xinchu Fu

    (Department of Mathematics, Shanghai University, Shanghai 200072, China)

Abstract

In this paper, a three-dimensional (3D) autonomous chaotic system is introduced and analyzed. In the system, each equation contains a quadratic crossproduct. The system possesses a chaotic attractor with a large chaotic region. Importantly, the system can generate both one- and two-scroll chaotic attractors by choosing appropriate parameters. Some of its basic dynamical properties, such as the Lyapunov exponents, Lyapunov dimension, Poincaré maps, bifurcation diagram, and the chaotic dynamical behavior are studied by adjusting different parameters. Further, an equivalent electronic circuit for the proposed chaotic system is designed according to Kirchhoff’s Law, and a corresponding response electronic circuit is also designed for identifying the unknown parameters or monitoring the changes in the system parameters. Moreover, numerical simulations are presented to perform and complement the theoretical results.

Suggested Citation

  • Meng Liu & Zhaoyan Wu & Xinchu Fu, 2022. "Dynamical Analysis of a One- and Two-Scroll Chaotic System," Mathematics, MDPI, vol. 10(24), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4682-:d:999293
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    References listed on IDEAS

    as
    1. Wang, Ran & Li, Chunbiao & Kong, Sixiao & Jiang, Yicheng & Lei, Tengfei, 2022. "A 3D memristive chaotic system with conditional symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Zhou, Ling & You, Zhenzhen & Tang, Yun, 2021. "A new chaotic system with nested coexisting multiple attractors and riddled basins," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Huang, Kuifei & Yang, Qigui, 2009. "Stability and Hopf bifurcation analysis of a new system," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 567-578.
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    Cited by:

    1. García-Grimaldo, Claudio & Campos-Cantón, Eric, 2023. "Exploring a family of Bernoulli-like shift chaotic maps and its amplitude control," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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